Explicit nonsymmetric robust cycling bound

Derive an explicit bound for robust perceptron cycling with a coercive nonsymmetric linear score operator, complementing the qualitative bound established for finite update sets and quantifying its dependence on the geometry of the update set and the skew-symmetric part of the operator.

Background

The main robust perceptron cycling theorem proves the existence of a constant $C(E,U,A)$ controlling all approximate trajectories when the update set $U$ is finite, $0in\operatorname{conv}U$, and the linear operator $A$ is coercive but not necessarily symmetric. The proof uses compactness and finite coverings, so the resulting constant is qualitative rather than explicit.

An explicit estimate is available in the symmetric positive-definite case through a relative-inradius argument. For nonsymmetric operators, the paper identifies the ratio between the skew-symmetric part and the smallest eigenvalue of the symmetric part as a natural parameter, but does not establish a uniform quantitative dependence on that ratio.